Stability of an inverse problem for the discrete wave equation and\n convergence results

2013/10/18 by Lucie Baudouin, Sylvain Ervedoza, Baudouin, Lucie +3 · 1 citation
Computer Science · Engineering · Mathematics · #Advanced Mathematical Modeling in Engineering #Analysis of PDEs (math.AP) #FOS: Mathematics #Numerical methods in inverse problems #Stability and Controllability of Differential Equations

paper · pdf · doi:10.48550/arxiv.1310.5092

openalex publication_date 2013/10/18 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Using uniform global Carleman estimates for discrete elliptic and\nsemi-discrete hyperbolic equations, we study Lipschitz and logarithmic\nstability for the inverse problem of recovering a potential in a semi-discrete\nwave equation, discretized by finite differences in a 2-d uniform mesh, from\nboundary or internal measurements. The discrete stability results, when\ncompared with their continuous counterparts, include new terms depending on the\ndiscretization parameter h. From these stability results, we design a numerical\nmethod to compute convergent approximations of the continuous potential.\n

Citations

• Propagation, Observation, and Control of Waves Approximated by Finite Difference Methods
• Stabilisation de l’équation des ondes par le bord
• Boundary observability for the space semi-discretizations of the 1 – d wave equation

Cited by

• Lipschitz stability for an inverse problem of a fully-discrete stochastic hyperbolic equation

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• Convergence of an inverse problem for discrete wave equations
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• Lipschitz stability for an inverse problem of a fully-discrete stochastic hyperbolic equation